Asymptotic Safety (to nonperturbatively renormalize gravity) the idea is to get a predictive theory, where you only have to specify the values of a finite number of physically meaningful parameters---experimentally determined--and from there on your theory predicts stuff. and it is NOT based on a perturbative powerseries expansion with "first order, second order" etc. terms. so the usual talk about diagrams for calculating terms in the series, one-loop and two-loop etc... that usual talk doesn't apply in this context. Because it is a different kind of renormalization, which Reuter and his bunch calle NONperturbative. The idea was originally due to Steven Weinberg who tried it back in 1976-1979 and Weinberg called it ASYMPTOTIC SAFETY. Basically what that means is you find a fixed point in the renormalization flow that allows your theory to be predictive after some finite number of parameters are specified. Judging from Percacci's recent work it looks like the number of parameters is turning out to be something like THREE. WELL NOW IT LOOKS LIKE THERE IS GOING TO BE A PERCACCI CHAPTER IN ORITI'S BOOK http://arxiv.org/abs/0709.3851 Asymptotic Safety R. Percacci To appear in "Approaches to Quantum Gravity: Towards a New Understanding of Space, Time and Matter", ed. D. Oriti, Cambridge University Press (Submitted on 24 Sep 2007) "Asymptotic safety is a set of conditions, based on the existence of a nontrivial fixed point for the renormalization group flow, which would make a quantum field theory consistent up to arbitrarily high energies. After introducing the basic ideas of this approach, I review the present evidence in favor of an asymptotically safe quantum field theory of gravity".